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<p>Here, we define the math operation for thin structure dynamics.  
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &quot;all_particle_dynamics.h&quot;</code><br />
<code>#include &quot;<a class="el" href="elastic__solid_8h_source.html">elastic_solid.h</a>&quot;</code><br />
<code>#include &quot;<a class="el" href="weakly__compressible__fluid_8h_source.html">weakly_compressible_fluid.h</a>&quot;</code><br />
<code>#include &quot;<a class="el" href="base__kernel_8h_source.html">base_kernel.h</a>&quot;</code><br />
</div>
<p><a href="thin__structure__math_8h_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
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Namespaces</h2></td></tr>
<tr class="memitem:namespace_s_p_h"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespace_s_p_h.html">SPH</a></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a25a33ee7e23ffafa90ab86955c394f90"><td class="memItemLeft" align="right" valign="top">Vec2d&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="thin__structure__math_8cpp.html#a25a33ee7e23ffafa90ab86955c394f90">SPH::thin_structure_dynamics::getVectorAfterThinStructureRotation</a> (const Vec2d &amp;initial_vector, const Vec2d &amp;rotation_angles)</td></tr>
<tr class="memdesc:a25a33ee7e23ffafa90ab86955c394f90"><td class="mdescLeft">&#160;</td><td class="mdescRight">Each of these basic vector rotations appears counterclockwise.  <a href="thin__structure__math_8cpp.html#a25a33ee7e23ffafa90ab86955c394f90">More...</a><br /></td></tr>
<tr class="separator:a25a33ee7e23ffafa90ab86955c394f90"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aef8c7db2afd1bc1f827bd6bf67a2cd2b"><td class="memItemLeft" align="right" valign="top">Vec3d&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="thin__structure__math_8cpp.html#aef8c7db2afd1bc1f827bd6bf67a2cd2b">SPH::thin_structure_dynamics::getVectorAfterThinStructureRotation</a> (const Vec3d &amp;initial_vector, const Vec3d &amp;rotation_angles)</td></tr>
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Vec3d&#160;</td><td class="memItemRight" valign="bottom"><b>SPH::thin_structure_dynamics::getRotationFromPseudoNormalForFiniteDeformation</b> (const Vec3d &amp;dpseudo_n_d2t, const Vec3d &amp;rotation, const Vec3d &amp;angular_vel, Real dt)</td></tr>
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<tr class="memitem:abe06d61bccc904d631b9a6f9fde3426a"><td class="memItemLeft" align="right" valign="top"><a id="abe06d61bccc904d631b9a6f9fde3426a"></a>
Vec3d&#160;</td><td class="memItemRight" valign="bottom"><b>SPH::thin_structure_dynamics::getRotationFromPseudoNormalForSmallDeformation</b> (const Vec3d &amp;dpseudo_n_d2t, const Vec3d &amp;rotation, const Vec3d &amp;angular_vel, Real dt)</td></tr>
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Vec3d&#160;</td><td class="memItemRight" valign="bottom"><b>SPH::thin_structure_dynamics::getNormalFromDeformationGradientTensor</b> (const Mat3d &amp;F)</td></tr>
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<tr class="separator:a2f217f2b208ab1f336cc1b00723935d2"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a class="el" href="class_vecd.html">Vecd</a>&#160;</td><td class="memItemRight" valign="bottom"><b>SPH::thin_structure_dynamics::getWENOVariableJump</b> (const <a class="el" href="class_vecd.html">Vecd</a> &amp;e_ij, const Real &amp;r_ij, const <a class="el" href="class_vecd.html">Vecd</a> &amp;particle_i_value, const Matd &amp;gradient_particle_i_value, const <a class="el" href="class_vecd.html">Vecd</a> &amp;particle_j_value, const Matd &amp;gradient_particle_j_value)</td></tr>
<tr class="separator:a3d48cb5377ae96ced6e74fc3f93494f3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa53a80b9e112974841818c57f14bf565"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_vecd.html">Vecd</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="thin__structure__math_8cpp.html#aa53a80b9e112974841818c57f14bf565">SPH::thin_structure_dynamics::getWENOStateWithStencilPoints</a> (const <a class="el" href="class_vecd.html">Vecd</a> &amp;v1, const <a class="el" href="class_vecd.html">Vecd</a> &amp;v2, const <a class="el" href="class_vecd.html">Vecd</a> &amp;v3, const <a class="el" href="class_vecd.html">Vecd</a> &amp;v4)</td></tr>
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<a class="el" href="class_vecd.html">Vecd</a>&#160;</td><td class="memItemRight" valign="bottom"><b>SPH::thin_structure_dynamics::getWENORightState</b> (const <a class="el" href="class_vecd.html">Vecd</a> &amp;e_ij, const Real &amp;r_ij, const <a class="el" href="class_vecd.html">Vecd</a> &amp;particle_i_value, const Matd &amp;gradient_particle_i_value, const <a class="el" href="class_vecd.html">Vecd</a> &amp;particle_j_value, const Matd &amp;gradient_particle_j_value)</td></tr>
<tr class="separator:a804061a34feb0b5da7e781ed3ab7e15b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac40bea3e1f1e143b34aa507fefc5536c"><td class="memItemLeft" align="right" valign="top">Vec2d&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="thin__structure__math_8cpp.html#ac40bea3e1f1e143b34aa507fefc5536c">SPH::thin_structure_dynamics::getRotationJump</a> (const Vec2d &amp;pseudo_n_jump, const Mat2d &amp;transformation_matrix)</td></tr>
<tr class="separator:ac40bea3e1f1e143b34aa507fefc5536c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a006f436889e6ff2ee5e909153991a6d9"><td class="memItemLeft" align="right" valign="top"><a id="a006f436889e6ff2ee5e909153991a6d9"></a>
Vec3d&#160;</td><td class="memItemRight" valign="bottom"><b>SPH::thin_structure_dynamics::getRotationJump</b> (const Vec3d &amp;pseudo_n_jump, const Mat3d &amp;transformation_matrix)</td></tr>
<tr class="separator:a006f436889e6ff2ee5e909153991a6d9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8de94c902e1d07ef64a3ade158d91cc2"><td class="memItemLeft" align="right" valign="top">Mat2d&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="thin__structure__math_8cpp.html#a8de94c902e1d07ef64a3ade158d91cc2">SPH::thin_structure_dynamics::getCorrectedAlmansiStrain</a> (const Mat2d &amp;current_local_almansi_strain, const Real &amp;nu_)</td></tr>
<tr class="separator:a8de94c902e1d07ef64a3ade158d91cc2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ace5ac63dd9e41c543ced6abfa3ab9536"><td class="memItemLeft" align="right" valign="top"><a id="ace5ac63dd9e41c543ced6abfa3ab9536"></a>
Mat3d&#160;</td><td class="memItemRight" valign="bottom"><b>SPH::thin_structure_dynamics::getCorrectedAlmansiStrain</b> (const Mat3d &amp;current_local_almansi_strain, const Real &amp;nu_)</td></tr>
<tr class="separator:ace5ac63dd9e41c543ced6abfa3ab9536"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Here, we define the math operation for thin structure dynamics. </p>
<dl class="section author"><dt>Author</dt><dd>Dong Wu and Xiangyu Hu </dd></dl>
<dl class="section version"><dt>Version</dt><dd>0.1 </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="file_a8de94c902e1d07ef64a3ade158d91cc2"></a>
<h2 class="memtitle"><span class="permalink"><a href="#file_a8de94c902e1d07ef64a3ade158d91cc2">&#9670;&nbsp;</a></span>getCorrectedAlmansiStrain()</h2>

<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">Mat2d SPH::thin_structure_dynamics::getCorrectedAlmansiStrain </td>
          <td>(</td>
          <td class="paramtype">const Mat2d &amp;&#160;</td>
          <td class="paramname"><em>current_local_almansi_strain</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Real &amp;&#160;</td>
          <td class="paramname"><em>nu_</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">
<p>get the corrected Eulerian Almansi strain tensor according to plane stress problem. </p>

</div>
</div>
<a id="file_a2f217f2b208ab1f336cc1b00723935d2"></a>
<h2 class="memtitle"><span class="permalink"><a href="#file_a2f217f2b208ab1f336cc1b00723935d2">&#9670;&nbsp;</a></span>getLinearVariableJump()</h2>

<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname"><a class="el" href="class_vecd.html">Vecd</a> SPH::thin_structure_dynamics::getLinearVariableJump </td>
          <td>(</td>
          <td class="paramtype">const Vecd &amp;&#160;</td>
          <td class="paramname"><em>e_ij</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Real &amp;&#160;</td>
          <td class="paramname"><em>r_ij</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Vecd &amp;&#160;</td>
          <td class="paramname"><em>particle_i_value</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Matd &amp;&#160;</td>
          <td class="paramname"><em>gradient_particle_i_value</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Vecd &amp;&#160;</td>
          <td class="paramname"><em>particle_j_value</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Matd &amp;&#160;</td>
          <td class="paramname"><em>gradient_particle_j_value</em>&#160;</td>
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        <tr>
          <td></td>
          <td>)</td>
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</div><div class="memdoc">
<p>get variable jump form gradient tensor. </p>

</div>
</div>
<a id="file_a517398477499c3fce7a47dffeab2e92d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#file_a517398477499c3fce7a47dffeab2e92d">&#9670;&nbsp;</a></span>getNormalFromDeformationGradientTensor()</h2>

<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">Vec2d SPH::thin_structure_dynamics::getNormalFromDeformationGradientTensor </td>
          <td>(</td>
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          <td class="paramname"><em>F</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
</div><div class="memdoc">
<p>get the current normal direction from deformation gradient tensor. </p>

</div>
</div>
<a id="file_aa524ddbd5a6e463a2c81c3b4473d4ff6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#file_aa524ddbd5a6e463a2c81c3b4473d4ff6">&#9670;&nbsp;</a></span>getRotationFromPseudoNormalForFiniteDeformation()</h2>

<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">Vec2d SPH::thin_structure_dynamics::getRotationFromPseudoNormalForFiniteDeformation </td>
          <td>(</td>
          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>dpseudo_n_d2t</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>rotation</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Vec2d &amp;&#160;</td>
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        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">Real&#160;</td>
          <td class="paramname"><em>dt</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
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<p>get the rotation from pseudo-normal for finite deformation. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#file_a8b3fd329962c0fd43d4877fc318b881e">&#9670;&nbsp;</a></span>getRotationFromPseudoNormalForSmallDeformation()</h2>

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          <td class="memname">Vec2d SPH::thin_structure_dynamics::getRotationFromPseudoNormalForSmallDeformation </td>
          <td>(</td>
          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>dpseudo_n_d2t</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>rotation</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>angular_vel</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">Real&#160;</td>
          <td class="paramname"><em>dt</em>&#160;</td>
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          <td>)</td>
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<p>get the rotation from pseudo-normal for small deformation. </p>

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<a id="file_ac40bea3e1f1e143b34aa507fefc5536c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#file_ac40bea3e1f1e143b34aa507fefc5536c">&#9670;&nbsp;</a></span>getRotationJump()</h2>

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          <td class="memname">Vec2d SPH::thin_structure_dynamics::getRotationJump </td>
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          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>pseudo_n_jump</em>, </td>
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          <td class="paramtype">const Mat2d &amp;&#160;</td>
          <td class="paramname"><em>transformation_matrix</em>&#160;</td>
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<p>get the artificial rotation from the pseudo-normal jump. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#file_a25a33ee7e23ffafa90ab86955c394f90">&#9670;&nbsp;</a></span>getVectorAfterThinStructureRotation() <span class="overload">[1/2]</span></h2>

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          <td class="paramname"><em>initial_vector</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>rotation_angles</em>&#160;</td>
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<p>Each of these basic vector rotations appears counterclockwise. </p>
<p>getVectorAfterThinStructureRotation when the axis about which they occur points toward the observer, and the coordinate system is right-handed. </p>
<p>The rotation matrix. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#file_aef8c7db2afd1bc1f827bd6bf67a2cd2b">&#9670;&nbsp;</a></span>getVectorAfterThinStructureRotation() <span class="overload">[2/2]</span></h2>

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          <td>(</td>
          <td class="paramtype">const Vec3d &amp;&#160;</td>
          <td class="paramname"><em>initial_vector</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Vec3d &amp;&#160;</td>
          <td class="paramname"><em>rotation_angles</em>&#160;</td>
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<p>The rotation matrix about the X-axis. <br />
 The rotation matrix about the Y-axis. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#file_a367237431bca151646b6c5c810be8682">&#9670;&nbsp;</a></span>getVectorChangeRateAfterThinStructureRotation() <span class="overload">[1/2]</span></h2>

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          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>initial_vector</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>rotation_angles</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Vec2d &amp;&#160;</td>
          <td class="paramname"><em>angular_vel</em>&#160;</td>
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<p>Vector change rate after rotation. </p>
<p>The derivative of the rotation matrix. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#file_ad48ab0cead05dd6e6d2b2383b81a445b">&#9670;&nbsp;</a></span>getVectorChangeRateAfterThinStructureRotation() <span class="overload">[2/2]</span></h2>

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          <td class="paramtype">const Vec3d &amp;&#160;</td>
          <td class="paramname"><em>initial_vector</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Vec3d &amp;&#160;</td>
          <td class="paramname"><em>rotation_angles</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">const Vec3d &amp;&#160;</td>
          <td class="paramname"><em>angular_vel</em>&#160;</td>
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<p>The rotation matrix about the X-axis. <br />
<br />
<br />
 The rotation matrix about the Y-axis. <br />
<br />
 The derivative of the rotation matrix of the X-axis. <br />
 The derivative of the rotation matrix of the Y-axis. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#file_aa53a80b9e112974841818c57f14bf565">&#9670;&nbsp;</a></span>getWENOStateWithStencilPoints()</h2>

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          <td class="memname"><a class="el" href="class_vecd.html">Vecd</a> SPH::thin_structure_dynamics::getWENOStateWithStencilPoints </td>
          <td>(</td>
          <td class="paramtype">const Vecd &amp;&#160;</td>
          <td class="paramname"><em>v1</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">const Vecd &amp;&#160;</td>
          <td class="paramname"><em>v2</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">const Vecd &amp;&#160;</td>
          <td class="paramname"><em>v3</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">const Vecd &amp;&#160;</td>
          <td class="paramname"><em>v4</em>&#160;</td>
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          <td>)</td>
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<p>predict mid-point value by applying WENO reconstruction. </p>

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